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arXiv · 2102.04672

Native Type Theory

Christian Williams·Michael Stay
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Abstract

Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad class of languages, lambda-theories with equality, by embedding such a theory into the internal language of its topos of presheaves. Native types provide total specification of the structure of terms; and by internalizing transition systems, native type systems serve to reason about structure and behavior simultaneously. The construction is functorial, thereby providing a shared framework of higher-order reasoning for many languages, including programming languages.

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Christian Williams, Michael Stay. 2021-02-09. Native Type Theory. https://doi.org/10.4204/eptcs.372.9

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